In this paper, we propose DeepCut, a method to obtain pixelwise object segmentations given an image dataset labelled weak annotations, in our case bounding boxes. It extends the approach of the well-known GrabCut[1] method to include machine learning by training a neural network classifier from bounding box annotations. We formulate the problem as an energy minimisation problem over a densely-connected conditional random field and iteratively update the training targets to obtain pixelwise object segmentations. Additionally, we propose variants of the DeepCut method and compare those to a naïve approach to CNN training under weak supervision. We test its applicability to solve brain and lung segmentation problems on a challenging fetal magnetic resonance dataset and obtain encouraging results in terms of accuracy.